to determine the salvage value S(t), in dollars, of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely?
To determine the time it will take for the blender to depreciate completely, we need to find the value of t when the salvage value (S(t)) of the blender is zero dollars.
However, without specific details about the depreciation method or rate, we cannot provide a precise answer. Depreciation can be calculated using various methods, such as straight-line depreciation, declining balance depreciation, or sum-of-the-years' digits depreciation.
In the case of straight-line depreciation, where the asset depreciates by the same amount each year, we can use the following formula:
S(t) = P - (R * t)
Where:
S(t) is the salvage value of the blender after t years
P is the initial purchase price of the blender
R is the annual depreciation rate
t is the number of years since the purchase
To find the time it takes for the blender to depreciate completely (S(t) = 0), we can set the equation equal to zero and solve for t:
0 = P - (R * t)
R * t = P
t = P / R
Therefore, the time it will take for the blender to depreciate completely is given by dividing the initial purchase price (P) by the annual depreciation rate (R).